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HOUSTON (CBSDFW.COM) – Tea Party darling Ted Cruz is making national headlines today. He soundly defeated Lieutenant Governor David Dewhurst last night in the Republican race for U.S. Senate – 56 to 44 percent.

And this November, Cruz is favored to beat Democrat Paul Sadler.

This was a huge upset for Cruz, and on Wednesday many of the national news outlets spent the day talking and writing about Cruz’s big victory.

Supporters erupted in celebration last night when Cruz walked onto the stage and thanked them.

Cruz credits Tea Party members and grassroots conservatives with carrying him to victory over Dewhurst.

On Wednesday, Cruz told reporters the turnout of more than one million people was impressive, and that the Tea Party is unfairly portrayed as radical extremists.

“The Tea Party are everyday Texans, everyday Americans that believe in common sense answers living with our means. The Tea Party is helping bring the Republican Party back to the policies we should have been defending in the first place.”

Texas Democratic Party Chairman Gilberto Hinojosa quickly lashed out at Cruz. “A Ted Cruz victory is the absolute worst thing that could have happened to Texas Republicans. The inmates are officially running the asylum. Cruz is the anti-Latino Latino. In his bid for the Senate, Cruz launched constant unrelenting attacks on the Hispanic community.”

Texas Tea Party Caucus Advisory Board member Katrina Pierson, a Tea Party leader here in North Texas, says Cruz’s victory stunned the Republican establishment in Washington. “I don’t know if Washington is going to take a step back and re-evaluate things, or if they’re just going to do what Lieutenant Governor David Dewhurst did and ride it out.”

She says their next goal is to focus their energy on the state legislature in Austin.

Dewhurst outspent Cruz by nearly three to one. But he couldn’t out-run Cruz and all of his enthusiastic supporters.

Political analyst John Weekley says Dewhurst mistakenly ran as an incumbent. “When you’re running a grassroots campaign, it’s honestly easier to fire up your troops taking the castle on the hill than it is to defend the castle on the hill being shot at constantly.”

Weekley says Dewhurst didn’t show up at a lot of candidate forums to debate the issues.

Because the redistricting fight in Texas delayed the primary from early March to late May, many analysts think Cruz could not have won back in March, but the extra time gave him a chance.

Analysts say Dewhurst would likely have won, because Cruz was further behind in the polls. All of the negative ads he ran against Cruz may have backfired, and only angered Cruz’s supporters, and put-off Dewhurst’s own supporters.